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## Modelling Underwater Acoustics

Near-field to far-field prediction for underwater acoustics.

Manufacturers of underwater acoustic transducers want to know the performance characteristics of their devices in the acoustic far-field. However, for some transducers, direct measurement in the far-field requires a large volume of water such as a lake or reservoir, which means making test measurements is an expensive and time-consuming task.

Figure 1: The NPL open tank
for underwater acoustics in use.

## Introduction

As a solution to this problem, NPL has been investigating methods for predicting the far-field response of a transducer from measurements made in the near-field in a laboratory tank. NPL operates a large open tank (5.5m diameter, 5m deep, see Figure 1) equipped with a high-resolution positioning system, which is used for the near-field measurement scans.

## The Science

The propagation of acoustic waves of constant frequency in homogeneous media may be described using the Helmholtz equation, which can be reformulated as an integral equation over a closed surface. This means that if the pressure distribution over a closed surface is known, the pressure value anywhere else can be calculated.

Boundary element methods provide a numerical technique for solving the Helmholtz integral equation, and NPL has carried out an investigation of such methods. An initial study identified two techniques that were suitable for this problem, and work has concentrated on the validation and comparison of these two methods. Software is currently being developed that will process the scanning device output and calculate results at user-specified points in the far-field.

## Results &amp; Next Steps

The pictures below show a typical example of a measurement data set on a cylinder (figure 2) made up of about 29000 points and a far field prediction (figure 3) on a cylinder with a radius 20 times larger, calculated using about 7200 values. The next areas of investigation will be uncertainty estimation and understanding how the results depend on the number and distribution of measurement points.

 Figure 2: Measurement data. Figure 3: far-field prediction.

Click either image to see full-size.